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- W2056552920 abstract "Let E / F be a CM extension of number fields, and L be a positive definite binary hermitian lattice over the ring of integers of E . An element in F is called an exception of L if it is represented by every localization of L but not by L itself. We show that if E / F and a positive integer k are given, then there are only finitely many similarity classes of positive definite binary hermitian lattices with at most k exceptions. This generalizes the corresponding finiteness result by Earnest and Khosravani [A.G. Earnest, A. Khosravani, Representation of integers by positive definite binary hermitian lattices over imaginary quadratic fields, J. Number Theory 62 (1997) 368–374, Theorem 2.2] for the case F = Q . We also prove that for a fixed totally real field F of odd degree over Q , there are only finitely many CM extensions E / F for which there exists a positive definite regular normal binary hermitian lattice over the ring of integers of E ." @default.
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- W2056552920 date "2007-05-01" @default.
- W2056552920 modified "2023-09-29" @default.
- W2056552920 title "Positive definite binary hermitian forms with finitely many exceptions" @default.
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- W2056552920 doi "https://doi.org/10.1016/j.jnt.2006.07.016" @default.
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